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The pizza restaurant business model continues to be highly profitable while offering exciting growth potential for the most popular brands, both in the U.S. and internationally.

Because pizza restaurants are seemingly everywhere -- according to FranchiseHelp.com there were about 65,000 pizza franchises in the U.S. as of 2012 -- it may not seem like an industry sector with a lot of growth potential.

It is. QSR Magazine reported in 2012 that pizza consumption grew 15% from 2010 as more than four in 10 consumers said that they eat pizza at least once a week, compared to 26% in 2010.

Today we check in with three established global pizza restaurants to get the deep dish about which company is taking full advantage of Americans' ongoing pizza passion. For added flavor, we will also look at an up-and-coming pizza restaurant concept.

Seeking global domino-tionDomino's Pizza(NYSE:DPZ) is a delivery and carryout pizza restaurant chain with more than 10,000 stores worldwide. It is considered the largest pizza delivery chain in the world. The company uses a franchise-driven business model, which is why it only has 390 company-owned stores.

For the third quarter of 2013, Domino's Pizza reported very strong domestic same-store sales growth of 5.4% compared to the same quarter last year. The company's international division reported same-store growth of 5%. Total revenue increased nearly 7% for the quarter as both same-store sales and store count rose.

Comparing this year's third quarter to the third quarter of last year, Domino's consistently-efficient operations stand out. In the third quarter of 2012, net income was a very healthy 6.9% of revenue. This increased to 7.6% in the third quarter of 2013 as cost of sales as a percentage of revenue dropped by 40 basis points. Net income rose nearly 18% year-over-year.

A number of operational factors combine to make this company so successful. The most fundamental is the low square footage of its restaurants and its low-cost restaurant layout. The delivery and takeout model does not require wait staff, for example, so the personnel cost is low.

The company has jumped on the chance to leverage mobile and online technology to build its business. Domino's said in its earnings release that 95% of smartphones can now access its ordering apps. In its October 2013 Investor Presentation, the company said that digital orders now account for around 40% of total sales.

Domino's has been wildly successful with expanding its franchise system, particularly internationally. Growth is driven by the attractiveness of the Domino model to potential franchisees who see that the company has "delivered" increased average EBITDA to domestic franchisees over the last four years.

International store count is up a whopping 54% just since 2007, with the number of international locations growing by 1,858 over that time. There should be no stopping the company's growth. Domino's sees opportunities for 2,600 more franchises in just its top 10 international markets.

Does papa know pizza best?Papa John's International(NASDAQ:PZZA) is smaller than Domino's by store count, but its growth has been similarly impressive. Revenue was up 6.4% in the third quarter compared to the year-ago quarter.

Comparable-store sales growth was nearly 2% in its North American segment and more than 8% internationally. International revenue soared 24% for the quarter.

Papa John's is also primarily franchise driven, with only 15% of the company's total 4,296 worldwide locations company-owned. Papa John's is making great strides with international expansion as well. Although international locations make up 24% of total units for Papa John's, new international units accounted for 48% of total new locations year-to-date.

For the third quarter, Papa John's took its 6.4% total revenue increase and extended it to a 9.6% increase in net income year-over-year. "Papa" might consider expanding his familiar marketing slogan to "Better Ingredients, Better Pizza, Better Operating Cost Control."

Don't blame it on the pizzaYum! Brands(NYSE:YUM) is a global restaurant colossus with nearly 40,000 restaurants spread across 130 countries under the KFC, Pizza Hut and Taco Bell brands.

Third-quarter results for the company were not too tasty, however, as net income dropped to $152 million compared to $471 million in the same quarter a year ago. Total revenue for the company declined 3% to $3.47 billion.

The company is extremely focused on international restaurant development, particularly in China, with store count growing 12% year-over-year to more than 6,000. The China division was the main cause of the company's weak quarterly results. Same-store sales declined 11% as a result of continued consumer worries about food safety of KFC chicken which drove same-store sales down 14% for that brand.

Pizza was a bright spot for Yum! Brands in the quarter, though, as Chinese same-store sales for Pizza Hut grew 5%.

And now for something completely differentPizza Inn Holdings is tiny compared to these other companies, but it has come up with an innovative concept that bears watching: Pie Five Pizza, which is a fast casual restaurant offering hand-crafted artisan style pizzas with gourmet-sounding sauces such as Tuscan Marinara.

Pie Five, so named because the pizza is made to order in five minutes or less, is the company's innovative concept for future development. Although at the end of the first fiscal 2014 quarter the company had only 18 of these restaurants in four states, there are 150 franchised units under contract in 11 states. Forbes.com named Pie Five Pizza one of the "10 Hot New Restaurant Chains from Established Brands."

What we learnedYum! Brands continues to have problems with declining sales in China, which will have a negative impact on earnings. The company in its guidance estimates a "high-single to low-double-digit percentage decline in full-year EPS versus prior year." This is particularly disappointing for a company that had 11 consecutive years of double-digit EPS growth up until this year.

Domino's and Papa John's are gaining popularity with both consumers and franchisees -- and they need both to succeed -- which makes them excellent choices for long-term investors.

I like Domino's slightly better because of its ability to maintain a rapid rate of store growth despite its size. Current brand strength, tremendous operating efficiency, and future growth potential are an unbeatable combination.